The court had ordered Prime Minister Raja Pervez Ashraf to comply by Wednesday with an order to write to authorities in Switzerland asking them to reopen multimillion dollar corruption probes into the president.
Ashraf's predecessor, Yousuf Raza Gilani, was thrown out of office for refusing to write to the Swiss and the court this month made veiled threats that the new premier could suffer the same fate.
But on Wednesday, Judge Asif Saeed Khosa adjourned the case until August 8 after the attorney general, representing the government, asked for time to make "serious and genuine efforts" to resolve the stand-off with the judiciary.
"We trust that it is not impossible to bridge the gap between stated positions of the two institutions," the judge said.
On Tuesday, the attorney general urged the court to withdraw its orders, calling them "un-implementable" and contrary to the constitution.
For more than two years, the government has resisted judges' demands to reopen investigations into Zardari, arguing he enjoys immunity as head of state.
The showdown could force elections before February 2013 when the government would become the first in Pakistan's history to complete an elected, full five-year mandate.
The allegations against Zardari date back to the 1990s, when he and his late wife, former premier Benazir Bhutto, are suspected of laundering $12 million allegedly paid in bribes by companies seeking customs inspection contracts.
In 2009, the court overturned a political amnesty that froze investigations into the president and other politicians, ordering that the cases be reopened.